Question

f(x)=x^2.
g(x)=x-3

a. Find gf(x)

b. Fing g^-1 (x)

c. Solve the equation gf(x)= g^-1 (x)

Answer 1

PLEEEEAAAAAAAAAASEEEEEEEE HELP!!!!!!!!!!!!!

Answer 2

does this mean
\[f\circ g(x)\]?

Answer 3

i.e.
\[f(g(x))\]

Answer 4

oops sorry it is
\[g(f(x))\] ok first step replace the generic f by the specific one, get
\[g(x^2)\] then evaluate g at x^2 get
\[g(x^2)=x^2-3\]

Answer 5

\[g(x)=x-3\] says to subtract 3, so
\[g^{-1}(x)=x+3\] says to add 3. does the opposite action

Answer 6

and finally
\[g(f(x))=g^{-1}(x)\] means
\[x^2-3=x+3\] making
\[x^2-x-6=0\]
\[(x+2)(x-3)=0\]
\[x=-2,x=3\]